After finding this question I have been researching as the other answers seem out of date.
The Google search API would be the obvious choice as quoted by other users however it is now been deprecated in favour of Custom Search API.
Although not obvious at first the Custom Search API does allow you to search the entire web. However the bad news is that the order of the results are not the same as a regular web search.
In conclusion it used to be possible however it is no longer. The new API (at a cost) will allow you to search the web to you will not be able to get the ranking back as required.